Smartphone rivals Apple Inc. and Samsung Electronics Co. have dueled over patents in courts around the globe. Now they are sparring in front of the Obama administration, which faces a looming decision on whether to veto a trade body's order blocking the U.S. sale of some Apple devices.

At issue is a June ruling from the U.S. International Trade Commission, an increasingly hot venue for patent fights, that said Apple infringed on a Samsung patent and ordered a ban on some older-model Apple iPhones and iPads. The trade body...